Pre-Algebra Examples Simplifying and Evaluating Expressions

Simplify

$(x^{2} + x - 3) \cdot (x^{2} - 4)$

Step 1

Expand $(x^{2} + x - 3) (x^{2} - 4)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x^{2} + x^{2} \cdot - 4 + x \cdot x^{2} + x \cdot - 4 - 3 x^{2} - 3 \cdot - 4$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 2.1.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 2} + x^{2} \cdot - 4 + x \cdot x^{2} + x \cdot - 4 - 3 x^{2} - 3 \cdot - 4$

Step 2.1.1.2

Add $2$ and $2$ .

$x^{4} + x^{2} \cdot - 4 + x \cdot x^{2} + x \cdot - 4 - 3 x^{2} - 3 \cdot - 4$

Step 2.1.2

Move $- 4$ to the left of $x^{2}$ .

$x^{4} - 4 \cdot x^{2} + x \cdot x^{2} + x \cdot - 4 - 3 x^{2} - 3 \cdot - 4$

Step 2.1.3

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.1.3.1

Multiply $x$ by $x^{2}$ .

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Step 2.1.3.1.1

Raise $x$ to the power of $1$ .

$x^{4} - 4 x^{2} + x^{1} x^{2} + x \cdot - 4 - 3 x^{2} - 3 \cdot - 4$

Step 2.1.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} - 4 x^{2} + x^{1 + 2} + x \cdot - 4 - 3 x^{2} - 3 \cdot - 4$

Step 2.1.3.2

Add $1$ and $2$ .

$x^{4} - 4 x^{2} + x^{3} + x \cdot - 4 - 3 x^{2} - 3 \cdot - 4$

Step 2.1.4

Move $- 4$ to the left of $x$ .

$x^{4} - 4 x^{2} + x^{3} - 4 \cdot x - 3 x^{2} - 3 \cdot - 4$

Step 2.1.5

Multiply $- 3$ by $- 4$ .

$x^{4} - 4 x^{2} + x^{3} - 4 x - 3 x^{2} + 12$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $3 x^{2}$ from $- 4 x^{2}$ .

$x^{4} - 7 x^{2} + x^{3} - 4 x + 12$

Step 2.2.2

Move $- 7 x^{2}$ .

$x^{4} + x^{3} - 7 x^{2} - 4 x + 12$

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